JEE Main2006MathematicsMatricesActual
Let A= ( array ll 1 & 2 3 & 4 array ) and B= ( array ll a & 0 0 & b array ), a, b N . Then
Options
- Athere cannot exist any B such that AB = BA
- Bthere exist more than one but finite number of B’s such that AB = BA
- Cthere exists exactly one B such that AB = BA
- Dthere exist infinitely many B’s such that AB = BA
Correct answer
D. there exist infinitely many B’s such that AB = BA
Step-by-step solution
A= [ array ll 1 & 2 3 & 4 array ] B= [ array ll a & 0 0 & b array ]A B= [ array ll a & 2 b 3 a & 4 b array ]B A= [ array ll a & 0 0 & b array ] [ array ll 1 & 2 3 & 4 array ]= [ array cc a & 2 a 3 b & 4 b array ]A B=B A only when a=b